| List-I (Precipitating reagent and conditions) | List-II (Cation) |
|---|---|
| (A) \(NH_4Cl + NH_4OH\) | (I) Mn2+ |
| (B) \(NH_4OH + Na_2CO_3\) | (II) Pb2+ |
| (C) \(NH_4OH + NH_4Cl + H_2S gas\) | (III) Al3+ |
| (D) dilute HCl | (IV) Sr2+ |
To solve the given problem, we need to match the reagents and conditions from List-I with the corresponding cations from List-II. Each reagent precipitates specific cations under given conditions:
Based on the information above, the correct matching is:
The correct option is A-III, B-IV, C-I, D-II.
The matching is based on the chemical properties and specific precipitation conditions for cations:
[A.] NH$_4$Cl + NH$_4$OH precipitates Al(OH)$_3$, hence matches with III. Al$^{3+}$.
[B.] NH$_4$OH + Na$_2$CO$_3$ precipitates SrCO$_3$, hence matches with IV. Sr$^{2+}$.
[C.] NH$_4$OH + NH$_4$Cl + H$_2$S gas precipitates PbS, hence matches with II. Pb$^{2+}$.
[D.] Dilute HCl precipitates MnCl$_2$, hence matches with I. Mn$^{2+}$.
Thus, the correct order is:
\[A -- III, B -- IV, C -- II, D -- I.\]
In the group analysis of cations, Ba$^{2+}$ & Ca$^{2+}$ are precipitated respectively as
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.